Properties

Label 12.96-7.0.2-4-48.3
Genus \(12\)
Quotient genus \(0\)
Group \(C_{48}:C_2\)
Signature \([ 0; 2, 4, 48 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $12$
Quotient genus: $0$
Group name: $C_{48}:C_2$
Group identifier: $[96,7]$
Signature: $[ 0; 2, 4, 48 ]$
Conjugacy classes for this refined passport: $3, 6, 22$

Jacobian variety group algebra decomposition:$A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s): $12, 20$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,4) (2,5) (3,6) (7,10) (8,11) (9,12) (13,16) (14,17) (15,18) (19,22) (20,23) (21,24) (25,28) (26,29) (27,30) (31,34) (32,35) (33,36) (37,40) (38,41) (39,42) (43,46) (44,47) (45,48) (49,52) (50,53) (51,54) (55,58) (56,59) (57,60) (61,64) (62,65) (63,66) (67,70) (68,71) (69,72) (73,76) (74,77) (75,78) (79,82) (80,83) (81,84) (85,88) (86,89) (87,90) (91,94) (92,95) (93,96)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{24}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.96-7.0.2-4-48.3.1

  (1,49) (2,51) (3,50) (4,52) (5,54) (6,53) (7,58) (8,60) (9,59) (10,55) (11,57) (12,56) (13,70) (14,72) (15,71) (16,67) (17,69) (18,68) (19,64) (20,66) (21,65) (22,61) (23,63) (24,62) (25,85) (26,87) (27,86) (28,88) (29,90) (30,89) (31,94) (32,96) (33,95) (34,91) (35,93) (36,92) (37,73) (38,75) (39,74) (40,76) (41,78) (42,77) (43,82) (44,84) (45,83) (46,79) (47,81) (48,80)
  (1,78,4,75) (2,77,5,74) (3,76,6,73) (7,81,10,84) (8,80,11,83) (9,79,12,82) (13,93,16,96) (14,92,17,95) (15,91,18,94) (19,87,22,90) (20,86,23,89) (21,85,24,88) (25,51,28,54) (26,50,29,53) (27,49,30,52) (31,60,34,57) (32,59,35,56) (33,58,36,55) (37,72,40,69) (38,71,41,68) (39,70,42,67) (43,66,46,63) (44,65,47,62) (45,64,48,61)
  (1,38,18,34,8,45,22,26,6,40,14,33,10,47,21,28,2,39,16,35,9,43,23,27,4,41,15,31,11,48,19,29,3,37,17,36,7,44,24,25,5,42,13,32,12,46,20,30) (49,86,66,82,56,93,70,74,54,88,62,81,58,95,69,76,50,87,64,83,57,91,71,75,52,89,63,79,59,96,67,77,51,85,65,84,55,92,72,73,53,90,61,80,60,94,68,78)